Can I say something from a SENCO perspective?
Senco in primary are often class teachers with no expertise. If they are lucky they will get to do some of the excellent senco training out there but in these days of tight budgets... The amount of paperwork a senco has to do is huge. Please do not underestimate this. I could spend all of my time on paper work (some of it pointless but have to justify and prove everything you do in case of inspection), however, actually, i'd like to teach children its what I'm good at.
Primary sencos are seldom trained in assessment. In secondary it is necessary so that exam access arrangements can be awarded. I put myself through the post grad cert for that at considerable cost. The hoops to jump through and expense to become a specialist teacher are huge and often beyond the reach of most.
To try and get over this problem, dyslexia screeners (using computers) are used. I think they are not great and don't use them myself but then I'm trained. Unfortunately, some people ignore good old fashioned observation, book scruitiny, listening to parents, asking the teacher, asking the child, and common sense. However, all these take time and that's something that most teachers don't have, particularly if the senco is also head of 6 other subject areas.
Private EP. Well here, I have to say, and I have a lot, and I mean a lot of evidence for this, that some do take the money and give the parents what they want to hear. I've got quite a few 'middle class dyslexics'. They have reading ages 5 years ABOVE their chronological ages, they write fluently, they are cohearant, their spelling is not great but within bog standard average scores, they do not need any special provision, they are above target in all areas (and we are talking targets of B and A grade.). I have read some truly poorly written reports. jCQ have got wise to this and so a private EP is now last on their list to award extra time. It is up to the schools specialist teacher to award or not exam access arrangements and much evidence is required.
A senco has to be pretty sure that a childwill get a diagnosis before recommending that parents spend money as I have known it happen that parents pay, don't get a diagnosis and then blame the school, despite there being evidence to suggest a particular need. Lea ed psychs are rare beasts who have to be booked and in my experience are a bit crap! Also to move on for disabled student allowance you need a report written in secondary. For exam access arrangements in secondary, where there is no one to assess, JCQ will only accept a report in secondary so sometimes staff don't want to ask a parent to pay twice.
Some parents won't accept a diagnosis. I have one child at the mo with major dyslexia whose mother is refusing to get her tested. I have heard of one case where the mother wouldn't allow the child to be on the sen register or receive extra help. In other words, you have to deal with very varied people!
That all being said, OP, your son sounds dyslexic to me with possible co morbid speech and language delay.
And finally, yes some sencos are rubbish just as I have to deal with some parents who, for whatever reason, are hopeless. The sadness comes is when a child who needs support gets stuck between a crap senco and hopeless parents. Your children have you lot fighting their corner, rattling cages and stamping feet, just like I do for my kids. It's very difficult when you know there is a problem, a solution, but your hands are tied.
Sorry for the rant but we do doa very difficult job which I think goes unacknowleged. We are often the person campaigning for 'our' students in school and being their advocates, often this causes annoyance because we have to demand and aggrevate to get them what they want. I spend countless hours pleading with leas for more money or support, cajoling staff to use different fonts, talking children out of a locked loo. Crikey, the list is endless.